A homogeneous differential equation of the form dx/dy = h(x/y) can be solved by making the substitution.

C — The correct option is (C). The provided text explicitly states in the Note that if a homogeneous differential equation is of the form dx/dy = F(x, y) (which corresponds to h(x/y)), we make the substitution x/y = v, which is equivalent to x = vy. This substitution transforms the equation into a form where variables can be separated and integrated.

A homogeneous differential equation of the form dx/dy = h(x/y) can…

Question 62 of 96beginner🧠 RememberMCQ1 mark

A homogeneous differential equation of the form $\frac{dx}{dy} = h\left(\frac{x}{y}\right)$ can be solved by making the substitution.

Exercise: EXERCISE 9.4 | Q: 16 | (Page 22)

For More Understanding

Explanation

The correct option is (C). The provided text explicitly states in the Note that if a homogeneous differential equation is of the form $\frac{dx}{dy} = F(x, y)$ (which corresponds to $h\left(\frac{x}{y}\right)$ ), we make the substitution $\frac{x}{y} = v$ , which is equivalent to $x = vy$ . This substitution transforms the equation into a form where variables can be separated and integrated.

Solution Steps

Step 1: Identify the form of the given differential equation: $\frac{dx}{dy} = h\left(\frac{x}{y}\right)$ .
Step 2: Refer to the Note in the text regarding equations of the form $\frac{dx}{dy} = F(x, y)$ .
Step 3: Apply the rule stated: make the substitution $\frac{x}{y} = v$ , which implies $x = vy$ .
Step 4: Match this substitution with the given options to select Option (C).

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